| 1 | MODULE diffusion_u_mod |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Current revisions: |
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| 5 | ! ----------------- |
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| 6 | ! |
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| 7 | ! |
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| 8 | ! Former revisions: |
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| 9 | ! ----------------- |
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| 10 | ! $Id: diffusion_u.f90 1017 2012-09-27 11:28:50Z raasch $ |
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| 11 | ! |
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| 12 | ! 1015 2012-09-27 09:23:24Z raasch |
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| 13 | ! accelerator version (*_acc) added |
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| 14 | ! |
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| 15 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 16 | ! arrays comunicated by module instead of parameter list |
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| 17 | ! |
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| 18 | ! 978 2012-08-09 08:28:32Z fricke |
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| 19 | ! outflow damping layer removed |
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| 20 | ! kmym_x/_y and kmyp_x/_y change to kmym and kmyp |
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| 21 | ! |
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| 22 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 23 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
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| 24 | ! |
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| 25 | ! 366 2009-08-25 08:06:27Z raasch |
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| 26 | ! bc_ns replaced by bc_ns_cyc |
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| 27 | ! |
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| 28 | ! 106 2007-08-16 14:30:26Z raasch |
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| 29 | ! Momentumflux at top (uswst) included as boundary condition, |
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| 30 | ! i loop is starting from nxlu (needed for non-cyclic boundary conditions) |
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| 31 | ! |
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| 32 | ! 75 2007-03-22 09:54:05Z raasch |
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| 33 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes, |
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| 34 | ! z0 removed from argument list, uxrp eliminated |
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| 35 | ! |
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| 36 | ! 20 2007-02-26 00:12:32Z raasch |
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| 37 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
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| 38 | ! |
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| 39 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 40 | ! |
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| 41 | ! Revision 1.15 2006/02/23 10:35:35 raasch |
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| 42 | ! nzb_2d replaced by nzb_u_outer in horizontal diffusion and by nzb_u_inner |
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| 43 | ! or nzb_diff_u, respectively, in vertical diffusion, |
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| 44 | ! wall functions added for north and south walls, +z0 in argument list, |
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| 45 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
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| 46 | ! because they cause errors at the edges of topography |
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| 47 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
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| 48 | ! |
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| 49 | ! Revision 1.1 1997/09/12 06:23:51 raasch |
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| 50 | ! Initial revision |
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| 51 | ! |
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| 52 | ! |
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| 53 | ! Description: |
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| 54 | ! ------------ |
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| 55 | ! Diffusion term of the u-component |
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| 56 | ! To do: additional damping (needed for non-cyclic bc) causes bad vectorization |
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| 57 | ! and slows down the speed on NEC about 5-10% |
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| 58 | !------------------------------------------------------------------------------! |
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| 59 | |
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| 60 | USE wall_fluxes_mod |
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| 61 | |
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| 62 | PRIVATE |
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| 63 | PUBLIC diffusion_u, diffusion_u_acc |
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| 64 | |
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| 65 | INTERFACE diffusion_u |
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| 66 | MODULE PROCEDURE diffusion_u |
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| 67 | MODULE PROCEDURE diffusion_u_ij |
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| 68 | END INTERFACE diffusion_u |
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| 69 | |
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| 70 | INTERFACE diffusion_u_acc |
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| 71 | MODULE PROCEDURE diffusion_u_acc |
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| 72 | END INTERFACE diffusion_u_acc |
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| 73 | |
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| 74 | CONTAINS |
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| 75 | |
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| 76 | |
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| 77 | !------------------------------------------------------------------------------! |
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| 78 | ! Call for all grid points |
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| 79 | !------------------------------------------------------------------------------! |
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| 80 | SUBROUTINE diffusion_u |
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| 81 | |
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| 82 | USE arrays_3d |
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| 83 | USE control_parameters |
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| 84 | USE grid_variables |
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| 85 | USE indices |
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| 86 | |
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| 87 | IMPLICIT NONE |
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| 88 | |
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| 89 | INTEGER :: i, j, k |
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| 90 | REAL :: kmym, kmyp, kmzm, kmzp |
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| 91 | |
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| 92 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs |
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| 93 | |
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| 94 | ! |
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| 95 | !-- First calculate horizontal momentum flux u'v' at vertical walls, |
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| 96 | !-- if neccessary |
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| 97 | IF ( topography /= 'flat' ) THEN |
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| 98 | CALL wall_fluxes( usvs, 1.0, 0.0, 0.0, 0.0, nzb_u_inner, & |
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| 99 | nzb_u_outer, wall_u ) |
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| 100 | ENDIF |
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| 101 | |
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| 102 | DO i = nxlu, nxr |
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| 103 | DO j = nys, nyn |
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| 104 | ! |
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| 105 | !-- Compute horizontal diffusion |
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| 106 | DO k = nzb_u_outer(j,i)+1, nzt |
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| 107 | ! |
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| 108 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 109 | kmyp = 0.25 * & |
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| 110 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 111 | kmym = 0.25 * & |
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| 112 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 113 | |
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| 114 | tend(k,j,i) = tend(k,j,i) & |
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| 115 | & + 2.0 * ( & |
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| 116 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 117 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 118 | & ) * ddx2 & |
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| 119 | & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 120 | & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 121 | & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 122 | & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 123 | & ) * ddy |
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| 124 | ENDDO |
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| 125 | |
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| 126 | ! |
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| 127 | !-- Wall functions at the north and south walls, respectively |
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| 128 | IF ( wall_u(j,i) /= 0.0 ) THEN |
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| 129 | |
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| 130 | DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) |
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| 131 | kmyp = 0.25 * & |
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| 132 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 133 | kmym = 0.25 * & |
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| 134 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 135 | |
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| 136 | tend(k,j,i) = tend(k,j,i) & |
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| 137 | + 2.0 * ( & |
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| 138 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 139 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 140 | ) * ddx2 & |
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| 141 | + ( fyp(j,i) * ( & |
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| 142 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 143 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 144 | ) & |
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| 145 | - fym(j,i) * ( & |
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| 146 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 147 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 148 | ) & |
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| 149 | + wall_u(j,i) * usvs(k,j,i) & |
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| 150 | ) * ddy |
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| 151 | ENDDO |
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| 152 | ENDIF |
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| 153 | |
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| 154 | ! |
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| 155 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 156 | !-- index k starts at nzb_u_inner+2. |
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| 157 | DO k = nzb_diff_u(j,i), nzt_diff |
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| 158 | ! |
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| 159 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 160 | kmzp = 0.25 * & |
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| 161 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 162 | kmzm = 0.25 * & |
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| 163 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 164 | |
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| 165 | tend(k,j,i) = tend(k,j,i) & |
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| 166 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 167 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 168 | & ) & |
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| 169 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 170 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 171 | & ) & |
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| 172 | & ) * ddzw(k) |
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| 173 | ENDDO |
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| 174 | |
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| 175 | ! |
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| 176 | !-- Vertical diffusion at the first grid point above the surface, |
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| 177 | !-- if the momentum flux at the bottom is given by the Prandtl law or |
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| 178 | !-- if it is prescribed by the user. |
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| 179 | !-- Difference quotient of the momentum flux is not formed over half |
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| 180 | !-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison |
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| 181 | !-- with other (LES) modell showed that the values of the momentum |
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| 182 | !-- flux becomes too large in this case. |
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| 183 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 184 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 185 | IF ( use_surface_fluxes ) THEN |
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| 186 | k = nzb_u_inner(j,i)+1 |
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| 187 | ! |
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| 188 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 189 | kmzp = 0.25 * & |
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| 190 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 191 | kmzm = 0.25 * & |
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| 192 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 193 | |
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| 194 | tend(k,j,i) = tend(k,j,i) & |
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| 195 | & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 196 | & ) * ddzw(k) & |
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| 197 | & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 198 | & + usws(j,i) & |
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| 199 | & ) * ddzw(k) |
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| 200 | ENDIF |
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| 201 | |
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| 202 | ! |
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| 203 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 204 | !-- if the momentum flux at the top is prescribed by the user |
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| 205 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 206 | k = nzt |
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| 207 | ! |
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| 208 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 209 | kmzp = 0.25 * & |
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| 210 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 211 | kmzm = 0.25 * & |
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| 212 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 213 | |
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| 214 | tend(k,j,i) = tend(k,j,i) & |
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| 215 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 216 | & ) * ddzw(k) & |
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| 217 | & + ( -uswst(j,i) & |
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| 218 | & - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 219 | & ) * ddzw(k) |
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| 220 | ENDIF |
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| 221 | |
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| 222 | ENDDO |
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| 223 | ENDDO |
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| 224 | |
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| 225 | END SUBROUTINE diffusion_u |
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| 226 | |
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| 227 | |
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| 228 | !------------------------------------------------------------------------------! |
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| 229 | ! Call for all grid points - accelerator version |
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| 230 | !------------------------------------------------------------------------------! |
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| 231 | SUBROUTINE diffusion_u_acc |
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| 232 | |
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| 233 | USE arrays_3d |
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| 234 | USE control_parameters |
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| 235 | USE grid_variables |
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| 236 | USE indices |
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| 237 | |
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| 238 | IMPLICIT NONE |
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| 239 | |
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| 240 | INTEGER :: i, j, k |
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| 241 | REAL :: kmym, kmyp, kmzm, kmzp |
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| 242 | |
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| 243 | !$acc declare create ( usvs ) |
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| 244 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs |
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| 245 | |
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| 246 | ! |
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| 247 | !-- First calculate horizontal momentum flux u'v' at vertical walls, |
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| 248 | !-- if neccessary |
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| 249 | IF ( topography /= 'flat' ) THEN |
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| 250 | CALL wall_fluxes_acc( usvs, 1.0, 0.0, 0.0, 0.0, nzb_u_inner, & |
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| 251 | nzb_u_outer, wall_u ) |
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| 252 | ENDIF |
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| 253 | |
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| 254 | !$acc kernels present ( u, v, w, km, tend, usws, uswst ) & |
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| 255 | !$acc present ( ddzu, ddzw, fym, fyp, wall_u ) & |
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| 256 | !$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u ) |
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| 257 | !$acc loop |
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| 258 | DO i = nxlu, nxr |
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| 259 | DO j = nys, nyn |
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| 260 | ! |
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| 261 | !-- Compute horizontal diffusion |
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| 262 | !$acc loop vector(32) |
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| 263 | DO k = 1, nzt |
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| 264 | IF ( k > nzb_u_outer(j,i) ) THEN |
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| 265 | ! |
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| 266 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 267 | kmyp = 0.25 * & |
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| 268 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 269 | kmym = 0.25 * & |
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| 270 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 271 | |
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| 272 | tend(k,j,i) = tend(k,j,i) & |
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| 273 | & + 2.0 * ( & |
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| 274 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 275 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 276 | & ) * ddx2 & |
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| 277 | & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 278 | & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 279 | & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 280 | & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 281 | & ) * ddy |
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| 282 | ENDIF |
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| 283 | ENDDO |
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| 284 | |
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| 285 | ! |
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| 286 | !-- Wall functions at the north and south walls, respectively |
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| 287 | !$acc loop vector(32) |
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| 288 | DO k = 1, nzt |
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| 289 | IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. & |
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| 290 | wall_u(j,i) /= 0.0 ) THEN |
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| 291 | |
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| 292 | kmyp = 0.25 * & |
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| 293 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 294 | kmym = 0.25 * & |
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| 295 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 296 | |
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| 297 | tend(k,j,i) = tend(k,j,i) & |
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| 298 | + 2.0 * ( & |
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| 299 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 300 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 301 | ) * ddx2 & |
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| 302 | + ( fyp(j,i) * ( & |
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| 303 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 304 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 305 | ) & |
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| 306 | - fym(j,i) * ( & |
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| 307 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 308 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 309 | ) & |
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| 310 | + wall_u(j,i) * usvs(k,j,i) & |
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| 311 | ) * ddy |
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| 312 | ENDIF |
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| 313 | ENDDO |
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| 314 | |
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| 315 | ! |
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| 316 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 317 | !-- index k starts at nzb_u_inner+2. |
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| 318 | !$acc loop vector(32) |
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| 319 | DO k = 1, nzt_diff |
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| 320 | IF ( k >= nzb_diff_u(j,i) ) THEN |
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| 321 | ! |
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| 322 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 323 | kmzp = 0.25 * & |
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| 324 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 325 | kmzm = 0.25 * & |
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| 326 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 327 | |
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| 328 | tend(k,j,i) = tend(k,j,i) & |
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| 329 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)& |
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| 330 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 331 | & ) & |
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| 332 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)& |
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| 333 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 334 | & ) & |
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| 335 | & ) * ddzw(k) |
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| 336 | ENDIF |
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| 337 | ENDDO |
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| 338 | |
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| 339 | ENDDO |
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| 340 | ENDDO |
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| 341 | |
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| 342 | ! |
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| 343 | !-- Vertical diffusion at the first grid point above the surface, |
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| 344 | !-- if the momentum flux at the bottom is given by the Prandtl law or |
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| 345 | !-- if it is prescribed by the user. |
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| 346 | !-- Difference quotient of the momentum flux is not formed over half |
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| 347 | !-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison |
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| 348 | !-- with other (LES) modell showed that the values of the momentum |
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| 349 | !-- flux becomes too large in this case. |
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| 350 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 351 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 352 | IF ( use_surface_fluxes ) THEN |
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| 353 | |
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| 354 | !$acc loop |
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| 355 | DO i = nxlu, nxr |
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| 356 | !$acc loop vector(32) |
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| 357 | DO j = nys, nyn |
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| 358 | |
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| 359 | k = nzb_u_inner(j,i)+1 |
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| 360 | ! |
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| 361 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 362 | kmzp = 0.25 * & |
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| 363 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 364 | kmzm = 0.25 * & |
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| 365 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 366 | |
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| 367 | tend(k,j,i) = tend(k,j,i) & |
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| 368 | & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 369 | & ) * ddzw(k) & |
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| 370 | & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 371 | & + usws(j,i) & |
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| 372 | & ) * ddzw(k) |
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| 373 | ENDDO |
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| 374 | ENDDO |
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| 375 | |
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| 376 | ENDIF |
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| 377 | |
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| 378 | ! |
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| 379 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 380 | !-- if the momentum flux at the top is prescribed by the user |
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| 381 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 382 | |
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| 383 | k = nzt |
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| 384 | |
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| 385 | !$acc loop |
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| 386 | DO i = nxlu, nxr |
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| 387 | !$acc loop vector(32) |
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| 388 | DO j = nys, nyn |
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| 389 | |
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| 390 | ! |
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| 391 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 392 | kmzp = 0.25 * & |
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| 393 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 394 | kmzm = 0.25 * & |
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| 395 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 396 | |
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| 397 | tend(k,j,i) = tend(k,j,i) & |
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| 398 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 399 | & ) * ddzw(k) & |
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| 400 | & + ( -uswst(j,i) & |
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| 401 | & - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 402 | & ) * ddzw(k) |
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| 403 | ENDDO |
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| 404 | ENDDO |
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| 405 | |
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| 406 | ENDIF |
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| 407 | !$acc end kernels |
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| 408 | |
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| 409 | END SUBROUTINE diffusion_u_acc |
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| 410 | |
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| 411 | |
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| 412 | !------------------------------------------------------------------------------! |
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| 413 | ! Call for grid point i,j |
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| 414 | !------------------------------------------------------------------------------! |
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| 415 | SUBROUTINE diffusion_u_ij( i, j ) |
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| 416 | |
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| 417 | USE arrays_3d |
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| 418 | USE control_parameters |
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| 419 | USE grid_variables |
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| 420 | USE indices |
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| 421 | |
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| 422 | IMPLICIT NONE |
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| 423 | |
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| 424 | INTEGER :: i, j, k |
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| 425 | REAL :: kmym, kmyp, kmzm, kmzp |
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| 426 | |
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| 427 | REAL, DIMENSION(nzb:nzt+1) :: usvs |
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| 428 | |
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| 429 | ! |
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| 430 | !-- Compute horizontal diffusion |
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| 431 | DO k = nzb_u_outer(j,i)+1, nzt |
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| 432 | ! |
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| 433 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 434 | kmyp = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 435 | kmym = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 436 | |
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| 437 | tend(k,j,i) = tend(k,j,i) & |
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| 438 | & + 2.0 * ( & |
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| 439 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 440 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 441 | & ) * ddx2 & |
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| 442 | & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 443 | & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 444 | & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 445 | & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 446 | & ) * ddy |
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| 447 | ENDDO |
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| 448 | |
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| 449 | ! |
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| 450 | !-- Wall functions at the north and south walls, respectively |
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| 451 | IF ( wall_u(j,i) .NE. 0.0 ) THEN |
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| 452 | |
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| 453 | ! |
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| 454 | !-- Calculate the horizontal momentum flux u'v' |
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| 455 | CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), & |
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| 456 | usvs, 1.0, 0.0, 0.0, 0.0 ) |
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| 457 | |
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| 458 | DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) |
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| 459 | kmyp = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 460 | kmym = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 461 | |
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| 462 | tend(k,j,i) = tend(k,j,i) & |
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| 463 | + 2.0 * ( & |
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| 464 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 465 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 466 | ) * ddx2 & |
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| 467 | + ( fyp(j,i) * ( & |
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| 468 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 469 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 470 | ) & |
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| 471 | - fym(j,i) * ( & |
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| 472 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 473 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 474 | ) & |
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| 475 | + wall_u(j,i) * usvs(k) & |
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| 476 | ) * ddy |
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| 477 | ENDDO |
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| 478 | ENDIF |
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| 479 | |
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| 480 | ! |
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| 481 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 482 | !-- index k starts at nzb_u_inner+2. |
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| 483 | DO k = nzb_diff_u(j,i), nzt_diff |
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| 484 | ! |
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| 485 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 486 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 487 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 488 | |
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| 489 | tend(k,j,i) = tend(k,j,i) & |
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| 490 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 491 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 492 | & ) & |
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| 493 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 494 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 495 | & ) & |
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| 496 | & ) * ddzw(k) |
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| 497 | ENDDO |
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| 498 | |
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| 499 | ! |
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| 500 | !-- Vertical diffusion at the first grid point above the surface, if the |
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| 501 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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| 502 | !-- prescribed by the user. |
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| 503 | !-- Difference quotient of the momentum flux is not formed over half of |
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| 504 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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| 505 | !-- other (LES) modell showed that the values of the momentum flux becomes |
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| 506 | !-- too large in this case. |
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| 507 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 508 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 509 | IF ( use_surface_fluxes ) THEN |
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| 510 | k = nzb_u_inner(j,i)+1 |
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| 511 | ! |
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| 512 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 513 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 514 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 515 | |
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| 516 | tend(k,j,i) = tend(k,j,i) & |
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| 517 | & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 518 | & ) * ddzw(k) & |
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| 519 | & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 520 | & + usws(j,i) & |
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| 521 | & ) * ddzw(k) |
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| 522 | ENDIF |
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| 523 | |
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| 524 | ! |
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| 525 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 526 | !-- if the momentum flux at the top is prescribed by the user |
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| 527 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 528 | k = nzt |
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| 529 | ! |
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| 530 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 531 | kmzp = 0.25 * & |
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| 532 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 533 | kmzm = 0.25 * & |
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| 534 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 535 | |
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| 536 | tend(k,j,i) = tend(k,j,i) & |
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| 537 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 538 | & ) * ddzw(k) & |
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| 539 | & + ( -uswst(j,i) & |
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| 540 | & - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 541 | & ) * ddzw(k) |
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| 542 | ENDIF |
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| 543 | |
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| 544 | END SUBROUTINE diffusion_u_ij |
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| 545 | |
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| 546 | END MODULE diffusion_u_mod |
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